Details

Time bar (total: 2.6m)

sample423.0ms

Algorithm
intervals
Results
168.0ms69×body1280valid
111.0ms52×body640valid
69.0ms195×body80valid
40.0ms35×body320valid
13.0ms17×body160valid

simplify302.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
302.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize39.0ms

Local error

Found 4 expressions with local error:

12.0b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
8.6b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
2.2b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (/ l t) (/ l t))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
79×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
18×associate-/l*
16×pow1
14×associate-*l*
13×swap-sqr associate-/r/
9×associate-*r/ div-inv
5×frac-times associate-*l/
4×pow-prod-down tan-quot insert-posit16 add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg flip3-+ *-commutative flip-+
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 246
Calls
4 calls:
Slowest
99.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
70.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
23.0ms
(* (/ l t) (/ l t))
11.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
843.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
265.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
49.0ms
(/ t (* (/ l t) (/ l t)))
41.0ms
(* (/ l t) (/ l t))

simplify49.2s

Counts
245 → 258
Calls
245 calls:
Slowest
2.2s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
1.6s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.6s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))))
1.3s
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))))

prune3.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.3b

localize80.0ms

Local error

Found 4 expressions with local error:

12.0b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.5b
(/ (sin k) (/ l t))
3.5b
(/ (sin k) (/ l t))
0.2b
(* (/ k t) (/ k t))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
415×times-frac
216×add-sqr-sqrt
206×add-cbrt-cube add-exp-log
204×*-un-lft-identity add-cube-cbrt
120×cbrt-undiv div-exp
46×prod-exp cbrt-unprod
39×div-inv
33×associate-/r*
21×associate-/l*
19×associate-/r/
13×swap-sqr associate-*r* associate-*l*
11×pow1
8×flip3-+ flip-+
4×insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up associate-/l/
Counts
4 → 406
Calls
4 calls:
Slowest
110.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
13.0ms
(/ (sin k) (/ l t))
13.0ms
(* (/ k t) (/ k t))
9.0ms
(/ (sin k) (/ l t))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
790.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
92.0ms
(/ (sin k) (/ l t))
89.0ms
(/ (sin k) (/ l t))
32.0ms
(* (/ k t) (/ k t))

simplify1.5m

Counts
568 → 418
Calls
568 calls:
Slowest
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.5s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.5s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
790.0ms
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))))
754.0ms
(/ (/ (sqrt 2) (* (cbrt (+ (* (/ k t) (/ k t)) 2)) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))))

prune6.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.0b

localize92.0ms

Local error

Found 4 expressions with local error:

11.3b
(sqrt (+ (* (/ k t) (/ k t)) 2))
11.3b
(sqrt (+ (* (/ k t) (/ k t)) 2))
9.3b
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
4.8b
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
14367×times-frac
5693×add-sqr-sqrt
5691×*-un-lft-identity add-cube-cbrt
1311×sqrt-prod
497×div-inv
367×associate-/r/
294×sqrt-div
181×add-exp-log
147×flip3-+ flip-+
143×associate-/r*
134×div-exp
81×add-cbrt-cube
53×cbrt-undiv
48×associate-/l*
25×1-exp
24×prod-exp
9×rec-exp
6×pow1 cbrt-unprod
4×insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 3743
Calls
4 calls:
Slowest
50.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
36.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
13.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
12.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series733.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
219.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
76.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
65.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))